# Self-answered questions as lemmas for an existing question

I've found an old question that I'd like to answer, on a subject I've investigated in the past.

But an answer will depend on two theorems I've not seen proved anywhere else (meaning I can't link to them). At least one of their proofs is quite long and needs several lemmas.

So I'm wondering about posting the theorems separately as "prove that . . . " questions, along with my proofs as answers, then linking to them when I answer the main question. My thought is that as well as de-cluttering the answer, it would help people who are interested just in the theorems to find them, and allow people with better proofs to post them.

Would this be considered an appropriate way to proceed in this kind of situation? An alternative would be to post the proofs on my blog and link to that, but I think really they belong here. On the other hand it seems slightly odd to post a question simply in order to post a proof.

It's an etiquette question, really. Is putting theorems in self-answered questions then linking to them an accepted way to behave?

Edit: the two theorems are self-contained things that I think people do want to know—one is an often stated fact about the game of Freecell, and the other states a situation in which the game is automatically won.

• Taking off my moderator hat for a moment, I think that posting two theorems as two questions, only for linking them to be used, is a bit excessive and borders on the treatment of this site as a personal blog. I wouldn't mind that if this was a natural progress (of natural questions, eventually leading to self-answers etc.), but posting for the sake of having a reference, seems a bit excessive. I'd just quote the theorems, without proof. Either they are simple enough that it doesn't matter, or they are worth writing properly and posting on arXiv or submitting somewhere, or someone proved them. – Asaf Karagila Feb 4 '19 at 18:14
• @AsafKaragila In this case I think the theorems are the main thing people ask about, so it wouldn't be just to have a reference, but I agree it seems a bit bloggish. I've amended my question to clarify about the theorems. – timtfj Feb 4 '19 at 18:40
• It seems totally reasonable to just write a long answer. Write the proofs after the main answer if you want to avoid clutter. – user98602 Feb 4 '19 at 20:09
• @Mike That seems reasonable—they're then just an appendix to the question. And only bother posting them elsewhere if they come up as "real" questions in their own right from a questioner. – timtfj Feb 4 '19 at 20:20
• I like joriki's take on this. When an answer otherwise becomes too long, this could save the day. But, I also share Asaf's concern that we should tread carefully, emphasizing what joriki said - Of course, this should only be done for sufficiently non-trivial results. – Jyrki Lahtonen Feb 7 '19 at 6:51
• I don't know how to best deal with your case. The impression I got, when reading joriki's post, was that the modularized parts could be used to answer several questions on our site. In your case that may not be the case. After all, we don't have very many questions about FreeCell (a fun solitary though it is). So, depending on how easily the question follows from those two theorems, I might suggest that you, in the first post, simply describe the two theorems, and show how that leads to an answer. – Jyrki Lahtonen Feb 7 '19 at 10:27
• Then, judging from the feedback you get, you can pretty much tell, whether extra posts, giving those proofs, would be received well. In other words, in your case I would consider posting the answer in three parts in that single thread. My thinking is that for you to post either of those theorems as self-answered questions, there should at least be some potential for more than one other question using the theorem. In yet other words, the self-answered question gets its justification from referrals. – Jyrki Lahtonen Feb 7 '19 at 10:31
• But, this is just my opinion. And even that is not frozen in place. I may have easily overlooked an aspect. +1 for asking, this may become a useful discussion. – Jyrki Lahtonen Feb 7 '19 at 10:33
• See also this. Alas,that discussion didn't really lift off the ground :-/ May be there are no pressing issues t be addressed? – Jyrki Lahtonen Feb 7 '19 at 10:34
• @Jyrki Maybe "in the same thread" could be done as multiple answers: "My main answer uses this . . . here's a proof of it"? That would be similar to when someone posts an answer adding a missing detail to the existing ones. I'm not sure I like it for something extended and arguably separste, though. – timtfj Feb 7 '19 at 15:07
• Further possibility: just one post, and summarise how the proofs work: "The proof involves showing $A, B, C$ then $D, E, F$" Anyone interested can then either try doing the proof or ask to see it. – timtfj Feb 7 '19 at 15:23
• Yes, that's what I meant. You can post three answers, and collect votes on each of them (as the voters see fit). Another reason to split the answer to several parts if that posting a single long post occasionally makes the MathJax previewer hog the CPU cycles. That was a worse problem back in the day. Typing used to become unbearably slow. They have been working on it, but you may still see it in a very long post with a lot of TeX, – Jyrki Lahtonen Feb 7 '19 at 17:53
• the most suitable way is probably posting your lemmas on your personal blog and then linking to them. In this way, you can post your lemmas freely and your answer would become more clear. – C.Ding Feb 15 '19 at 23:43
• @Cding Good point. It means I can write them as I want, without needing to worry about suitability for MSE, and include as much information as I think necessary. – timtfj Feb 16 '19 at 0:01
• To be honest, it looks like a good idea, even though the others are not agreeing with me. – onurcanbkts Feb 18 '19 at 16:29

Another option is post extremely short proof or proof sketches using overly advanced mathematics (like using FLT to prove $$\root 3 \of 2$$ is irrational) to save space, if possible. If someone wants a more readable proof, they can post a separate question, as in my first paragraph.